2024 · Q58
Consider the following for the next three (03) items that follow: Let MN be a chord of length 16 cm of a circle with centre at O and radius 10 cm. The tangents at M and N intersect at a point P. Further, OP intersects MN perpendicularly at Q. What is OQ equal to?
Elementary MathematicsGeometry: Lines, Angles and Triangles
- A5 cm
- B6 cm
- C7 cm
- D8 cm
Explanation
OP passes through the centre O and meets chord MN at right angles, so Q bisects MN and MQ = 8 cm. Triangle OQM is right-angled at Q with hypotenuse OM = 10 cm (radius). Hence OQ = √(10² − 8²) = √36 = 6 cm — option B.